



'''simple docstring'''



import math
def        UpperCAmelCase (    A	:					int					):
							SCREAMING_SNAKE_CASE       :   Tuple         =      math.loga(math.sqrt(4 * positive_integer + 1					) / 2 + 1 / 2					)

							return exponent == int(A					)
def        UpperCAmelCase (    A	:					float = 1 / 12345					):
							SCREAMING_SNAKE_CASE       :   List[Any]         =      0
							SCREAMING_SNAKE_CASE       :   Union[str, Any]         =      0

							SCREAMING_SNAKE_CASE       :   str         =      3
							while True:
														SCREAMING_SNAKE_CASE       :   List[str]         =      (integer**2 - 1) / 4
														# if candidate is an integer, then there is a partition for k
														if partition_candidate == int(A					):
																					SCREAMING_SNAKE_CASE       :   List[Any]         =      int(A					)
																					total_partitions += 1
																					if check_partition_perfect(A					):
																												perfect_partitions += 1
														if perfect_partitions > 0:
																					if perfect_partitions / total_partitions < max_proportion:
																												return int(A					)
														integer += 1


if __name__ == "__main__":
							print(f'{solution() = }')









'''simple docstring'''



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_torch_available,
)


lowerCAmelCase_  :							Dict             =    {
    'configuration_encodec': [
        'ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'EncodecConfig',
    ],
    'feature_extraction_encodec': ['EncodecFeatureExtractor'],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							lowerCAmelCase_  :							List[Any]             =    [
							    'ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST',
							    'EncodecModel',
							    'EncodecPreTrainedModel',
							]

if TYPE_CHECKING:
							from .configuration_encodec import (
							    ENCODEC_PRETRAINED_CONFIG_ARCHIVE_MAP,
							    EncodecConfig,
							)
							from .feature_extraction_encodec import EncodecFeatureExtractor

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_encodec import (
														    ENCODEC_PRETRAINED_MODEL_ARCHIVE_LIST,
														    EncodecModel,
														    EncodecPreTrainedModel,
														)

else:
							import sys

							lowerCAmelCase_  :							List[str]             =    _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




